de Sitter space

Warning. This is a concept which is more than a little abstruse. It is useful in any number of theoretical exercises, but rarely (if often) in practical reality. I have not been trained or educated as a physicist or astrophysicist or any other form of -cist, really. My explanation of the de Sitter space that follows is constructed from a wide variety of sources, including more knowledgeable friends attempting to explain it to me. Hence: caveat lector, and salt to taste. Real(tm) physics experts, please jump in to correct me where necessary.

Corrections have been offered by various folks, to whom I'm indebted. I await their more thorough and correct writeups so I can nuke this one (hint, hint!)

A de Sitter space is an astrophysics/cosmology construct. It describes a particular type of 'idealized' universe; that is, the simplest form of a universe described by solving the fundamental equations describing it symmetrically. Specifically, it is a universe ('space' in the astrophysics and cosmology game, apparently - what we would more likely call 'spacetime' thanks to good ol' Albert) where there is no matter, a uniform distribution of energy and a positive cosmological constant.

Our universe is, according to a remarkably uniform agreement among modern scientists (who never agree on anything, since it's bad for job prospects), currently expanding. There is a spirited debate as to whether the rate of that expansion is constant, slowing, or increasing (see Bekenstein bound for a fun example of why this matters). At base, it is possible to describe the forces acting on a universe with the following simple equation. Remember, by definition, those forces must be exerted from inside said universe, because if there is an 'outside' then it ain't a universe, nu? So, here we go:

Ω = ΩM + ΩΛ = 1 - ΩΚ

Translation: Ω (Everything) is equal to the sum of ΩM (matter, as in all the matter there is) plus ΩΛ - the cosmological constant, which includes vacuum energy. This is equal to 1 minus ΩΚ, or 1 minus the curvature. This curvature of spacetime is what determines whether the universe is closed, flat or open - that is, whether its rate of expansion is slowing, leading to a Big Crunch, whether the energies are balanced perfectly and it will continue to expand at the same rate forever, or whether the expansion is in fact speeding up as spacetime expands.

It's all over my head, too. Stick with me, almost there.

Now, Einstein didn't like the cosmological constant, and in fact repudiated it in his later work. If we accept that the universe is perfectly described by the equations of special relativity, and is flat, then there is no cosmological constant - it's zero. No quantum field energy, etc. Just the observable matter, which will lead to a curvature term. A universe such as this - pure special relativity - is called a Minkowski space.

Early in the twentieth century, a Dutchastronomer named Willem de Sitter was one of the first scientists to realize the implications of special relativity for the universe that science was able to observe. He set out to describe a universe which could, in fact, be expanding at increasing speed, despite being described (mostly) by special relativity. The result was de Sitter space - any space which, when described using the above equation, has a positive cosmological constant. In other words, a universe where space itself is positively curved even after all the possible perturbations due to mass and/or energy in the universe are removed due to the absolutely uniform distribution of said mass and energy.

Looked at one way, de Sitter space is a fully decayed (isotropic) space of pure energy, with infinite vector in every point, because the positive curvature of space-time means that each point will continue to accelerate away from every other point. Einstein-de Sitter space is the instance of de Sitter space where the cosmological constant is, in fact, zero; pure de Sitter space has a constant greater than one, and anti-de Sitter space has a negative cosmological constant and is hence headed for a Big Crunch.

Thanks for the corrections which have already started to roll in! Grzcyrgba informs me that vacuum energy is mo' def' not the same thing as cosmic microwave background radiation; rather, it is a "quantum mechanical fluctuation in empty space." Multiple folks offered speling corekshuns, needed after a latelatelatenight writeup.

Information for this writeup was taken from numerous patient explanations, diagrams on napkins, and several online references including:

The Cosmological Constant by Sean M. Caroll, online at http://www.livingreviews.org/Articles/Volume4/2001-1carroll

String Theory and Cosmology: de Sitter space-time foam by A. Starobinsky, online at the Nobel eMuseum at http://www.nobel.se/physics/symposia/ns127/abstract-starobinsky.html

Willem de Sitter, online blurb by the JapaneseNASDA at http://spaceboy.nasda.go.jp/note/kagaku/e/kag115_desitter_e.html

The String Theory landscape from PhysicsWeb at http://physicsweb.org/article/world/16/11/3